The invention is based on a device for attaching a screw cap to a container as defined hereinafter. In a device of this type known for instance from German Offenlegungsschrift No. 33 36 041, a slip coupling is disposed in the screw head, and if a predetermined capping and screwing torque is exceeded it releases the rotational connection with the driving motor. Additionally, the known device has detectors for ascertaining the rotational speed and the current supplied to the driving motor, as well as for measuring the torque applied. A device of this kind is expensive, and in the heavy-duty operation typical in bottling plants it tends to malfunction.